Lemma REF  can be seen as a generalisation of [1]} away from diffeological spaces to simplicial presheaves.
Indeed, the composition
\(\begin{tikzcd}{{D}\mathrm {fg}}[r, hookrightarrow, "\iota "] & {H}_\infty [r, "S_e"] & {{S}\mathrm {et}_{\hspace{-0.85355pt}\Delta }}\end{tikzcd}\) 
